The true value of each state-action pair, \(Q^{*}(s,a)\)  can be approximated iteratively by selecting actions at each time step.
In this work we select actions following the \(\varepsilon \) -greedy policy algorithm, where \(\varepsilon \)  is the probability of randomly selecting an action \(a\)  at each time step, and \((1-\varepsilon )\)  of greedily performing the action with the maximum expected reward determined by \({max}_aQ(s_t, a)\) .
The value of \(\varepsilon \)  starts from 1 and decreases towards a constant value \({min}_\varepsilon \)  at every time step.
After an action is selected \(Q(s_t, a_t)\)  is updated according to Eq. (REF ).
Note that \(Q\)  has been shown to converge to \(Q^{*}\)  [1]}, [2]}.
